This paper studies the pullback asymptotic behavior of solutions for a non-autonomous non-Newtonian fluid on \documentclass[12pt]{minimal}\begin{document}$\Omega = \mathbb {R}\times (-L, L)$\end{document}Ω=R×(−L,L) for some L > 0. We first use the technique of truncation functions together with the decomposition of spatial domain to prove the existence of a pullback attractor in Ω. Then we discuss the upper semicontinuity of the pullback attractors when the spatial domains vary from Ωm to Ω, where \documentclass[12pt]{minimal}\begin{document}$\lbrace \Omega _m\rbrace _{m=1}^\infty$\end{document}{Ωm}m=1∞ is an expanding sequence of simply connected, bounded, and smooth subdomains of Ω such that \documentclass[12pt]{minimal}\begin{document}$\cup _{m=1}^\infty \Omega _m=\Omega$\end{document}∪m=1∞Ωm=Ω. Let \documentclass[12pt]{minimal}\begin{document}$\hat{\mathcal {A}}=\lbrace \mathcal {A}(\tau )\rbrace _{\tau \in \mathbb {R}}$\end{document}Â={A(τ)}τ∈R and \documentclass[12pt]{minimal}\begin{document}$\hat{\mathcal {A}}_m=\lbrace \mathcal {A}_m(\tau )\rbrace _{\tau \in \mathbb {R}}$\end{document}Âm={Am(τ)}τ∈R be the pullback attractors corresponding to Ω and Ωm, respectively. We establish for each \documentclass[12pt]{minimal}\begin{document}$\tau \in \mathbb {R}$\end{document}τ∈R that for any neighborhood \documentclass[12pt]{minimal}\begin{document}$\mathcal {O}(\mathcal {A}(\tau ))$\end{document}O(A(τ)) of \documentclass[12pt]{minimal}\begin{document}$\mathcal {A}(\tau )$\end{document}A(τ), \documentclass[12pt]{minimal}\begin{document}$\mathcal {A}_m(\tau )$\end{document}Am(τ) enters \documentclass[12pt]{minimal}\begin{document}$\mathcal {O}(\mathcal {A}(\tau ))$\end{document}O(A(τ)) if m is large enough.